Input-selective Contraction Regulates Excitable Networks, Enabling Robust Stability and Digital-analog Reliability

The challenge of creating robust and efficient information processing systems draws inspiration from the animal nervous system, which seamlessly combines digital reliability with analog efficiency. Michelangelo Bin, Alessandro Cecconi, and Lorenzo Marconi, all from the University of Bologna and KU Leuven, investigate the fundamental principles underlying this capability. Their work reveals that the reliability of neuronal signals stems from a process of trajectory contraction, effectively focusing activity and reducing noise, and is directly influenced by incoming inputs. Importantly, the researchers demonstrate that this reliability enables excitable networks to self-regulate, achieving a stable and robust operating state, suggesting a pathway towards building dynamically adaptable and resilient systems.

Neuromorphic Control Inspired by Brain Resilience

This research investigates control systems inspired by the brain’s remarkable ability to maintain stability despite disturbances and noise, bridging the fields of control theory and computational neuroscience. It proposes Neuromorphic Control, a new approach that moves beyond traditional calibration-based methods, emphasizing reliable spike timing and synchronization as contributors to robust control, connecting these concepts with established contraction theory. The research demonstrates that internal models within these systems anticipate and adapt to disturbances, extending the concept of robustness to event-based control. The brain efficiently filters irrelevant information, leading to a more effective control strategy.

This interdisciplinary approach seamlessly integrates concepts from control theory, neuroscience, and dynamical systems, offering novel insights into designing robust and adaptive control systems. Potential areas for future exploration include hardware implementation using neuromorphic chips, application to real-world problems like robotics and autonomous vehicles, investigation of learning and adaptation mechanisms, and exploration of spiking neural networks as a platform for these control strategies. By bridging the gap between these fields, the authors have opened new avenues for designing robust, adaptive, and energy-efficient control systems, making it essential reading for anyone interested in the future of control theory and its applications.

Neuronal Reliability via Trajectory Contraction Analysis

Scientists investigated the relationship between reliability, contraction, and regulation within excitable systems, utilizing the FitzHugh-Nagumo model. They formalized neuronal reliability as an average trajectory contraction property induced by input signals, demonstrating how solutions converge or diverge. Experiments revealed that while solutions did not contract with a constant input, they maintained a constant phase shift, mirroring experimental observations. Introducing a harmonic frequency similar to the model’s natural oscillation resulted in reliable behavior due to resonance, sharpening spikes and increasing time spent in contraction regions.

Further experiments with a slow square wave input also demonstrated reliable behavior, as the forcing period significantly exceeded the natural oscillation period. Assessing robustness, the team simulated responses to Gaussian noisy inputs, finding that high noise fostered reliability due to resonance, while medium noise induced unreliability. To explore how reliability enables regulation, scientists constructed an excitatory-inhibitory (EI) network designed to reject disturbances. This network, embedding an internal model of the exosystem, demonstrated that reliability enables regulation, providing fundamental insight into the design of resilient biological and engineered systems.

Reliability Arises From Contraction and Resonance

This work demonstrates a fundamental connection between reliability, contraction, and regulation in excitable systems, mirroring principles observed in animal nervous systems. Researchers utilized the FitzHugh-Nagumo model to formalize neuronal reliability as an average trajectory contraction property induced by input signals. Experiments revealed that solutions originating from different initial conditions exhibit contraction, maintaining a constant phase shift when subjected to a constant input. Adding a harmonic frequency similar to the model’s natural oscillation resulted in reliable behavior due to resonance, sharpening spikes and increasing dwell time in contraction regions.

Further investigations with a slow square wave input also demonstrated reliable behavior, as the forcing period was significantly larger than the natural oscillation period. The team then simulated responses to Gaussian noisy inputs, finding that high noise fostered reliability, while medium noise induced unreliability. The research extends to an excitatory-inhibitory (EI) network, designed to reject disturbances through a control input. The team demonstrated that reliability enables regulation, establishing a crucial link between dynamical properties and robust control mechanisms, offering insights into the efficient and reliable operation of biological neural networks.

Neuronal Contraction Enables Robust Analog Computation

This research demonstrates a connection between neuronal reliability, network regulation, and robust computation, building upon the established FitzHugh-Nagumo model of excitable systems. The team formalized neuronal reliability as an average trajectory contraction property, revealing that this contraction enables the regulation of excitable networks to a stable steady state. This regulation is proposed as a form of dynamical computation, offering a robust, albeit analog, alternative to traditional digital approaches. The findings suggest that this model of computation is inherently input-selective, meaning stability depends on the input signal itself, a departure from classical control systems.

This input-selectivity offers potential advantages, including automatic filtering of relevant information and a natural multiresolution capability, where reliability emerges over timescales of multiple spikes. The authors propose that this principle could be implemented in redundant neural networks, where unreliable responses average to zero while reliable signals synchronize and propagate downstream. The researchers believe the core conclusions extend to more general conductance-based models and may serve as a foundation for a broader theory of reliable computation in neuromorphic systems. Future work could explore the implementation of these principles in more complex neural architectures and investigate the potential for robust adaptation and event-.